Catch trial performance

## [1] "Excluded 1 participants based on catch-trial performance."
## [1] "Excluded participants:"
## [1] 1529

Aggregated results

## `summarise()` has grouped output by 'workerid', 'percentage_blue', 'modal'. You
## can override using the `.groups` argument.
## `summarise()` has grouped output by 'percentage_blue', 'modal'. You can
## override using the `.groups` argument.
## `summarise()` has grouped output by 'workerid', 'percentage_blue', 'modal'. You
## can override using the `.groups` argument.

Comparison across conditions

## `summarise()` has grouped output by 'workerid', 'percentage_blue', 'modal'. You
## can override using the `.groups` argument.
## `summarise()` has grouped output by 'percentage_blue', 'modal'. You can
## override using the `.groups` argument.

Individual responses

AUC computation

We use the AUC function with the splines method to directly compute the AUC.

t-test and regression model with control variables:

## 
##  Two Sample t-test
## 
## data:  aucs.cautious$auc_diff and aucs.confident$auc_diff
## t = 3.5648, df = 126, p-value = 0.0005153
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   8.326556 29.108058
## sample estimates:
## mean of x mean of y 
## 20.693458  1.976151
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## auc_diff ~ cond + test_order + first_speaker_type + confident_speaker +  
##     first_speaker_type * cond + (1 | workerid)
##    Data: auc_d
## 
## REML criterion at convergence: 1180
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.32868 -0.50839  0.01431  0.64800  1.76492 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  workerid (Intercept) 335.3    18.31   
##  Residual             474.6    21.79   
## Number of obs: 128, groups:  workerid, 64
## 
## Fixed effects:
##                           Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)                 12.098      3.004 60.000   4.028 0.000161 ***
## cond1                        9.489      1.929 62.000   4.918 6.75e-06 ***
## test_order1                  1.833      3.010 60.000   0.609 0.544860    
## first_speaker_type1         -7.429      2.998 60.000  -2.478 0.016055 *  
## confident_speaker1          -5.887      3.007 60.000  -1.958 0.054871 .  
## cond1:first_speaker_type1   -2.090      1.929 62.000  -1.083 0.282873    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cond1  tst_r1 frs__1 cnfd_1
## cond1        0.000                            
## test_order1  0.060  0.000                     
## frst_spkr_1 -0.062  0.000 -0.007              
## cnfdnt_spk1 -0.024  0.000  0.092 -0.030       
## cnd1:frs__1  0.000 -0.062  0.000  0.000  0.000

Clustering analyses

library(mclust)
## Package 'mclust' version 5.4.10
## Type 'citation("mclust")' for citing this R package in publications.
## 
## Attaching package: 'mclust'
## The following object is masked from 'package:DescTools':
## 
##     BrierScore
## The following object is masked from 'package:bootstrap':
## 
##     diabetes
aucs_diff = merge(aucs.cautious, aucs.confident, by=c("workerid"))
aucs_diff$diff_of_diffs = aucs_diff$auc_diff.x - aucs_diff$auc_diff.y

aucs_diff %>% ggplot(aes(x=diff_of_diffs)) + geom_density() + geom_jitter(aes(y=0), width=0, height=0.001)  + ggtitle("Raw data + estimated density")

Gaussian mixture models of diffeences of AUC differences

1 Cluster

fit1 = Mclust(aucs_diff$diff_of_diffs, G=1)
print(summary(fit1, parameters=2))
## ---------------------------------------------------- 
## Gaussian finite mixture model fitted by EM algorithm 
## ---------------------------------------------------- 
## 
## Mclust X (univariate normal) model with 1 component: 
## 
##  log-likelihood  n df       BIC       ICL
##       -309.7775 64  2 -627.8728 -627.8728
## 
## Clustering table:
##  1 
## 64 
## 
## Mixing probabilities:
## 1 
## 1 
## 
## Means:
## [1] 18.71731
## 
## Variances:
## [1] 936.9875

2 Clusters

fit2 = Mclust(aucs_diff$diff_of_diffs, G=2)
print(summary(fit2, parameters=T))
## ---------------------------------------------------- 
## Gaussian finite mixture model fitted by EM algorithm 
## ---------------------------------------------------- 
## 
## Mclust E (univariate, equal variance) model with 2 components: 
## 
##  log-likelihood  n df     BIC       ICL
##       -304.2372 64  4 -625.11 -631.8846
## 
## Clustering table:
##  1  2 
## 56  8 
## 
## Mixing probabilities:
##         1         2 
## 0.8518197 0.1481803 
## 
## Means:
##         1         2 
##  9.268756 73.032642 
## 
## Variances:
##        1        2 
## 423.7863 423.7863

3 Clusters

fit3 = Mclust(aucs_diff$diff_of_diffs, G=3)
print(summary(fit3, parameters=T))
## ---------------------------------------------------- 
## Gaussian finite mixture model fitted by EM algorithm 
## ---------------------------------------------------- 
## 
## Mclust E (univariate, equal variance) model with 3 components: 
## 
##  log-likelihood  n df       BIC       ICL
##       -304.2422 64  6 -633.4377 -695.7058
## 
## Clustering table:
##  1  2  3 
## 10 46  8 
## 
## Mixing probabilities:
##         1         2         3 
## 0.3512637 0.5047542 0.1439820 
## 
## Means:
##         1         2         3 
##  4.325029 12.992664 73.897965 
## 
## Variances:
##        1        2        3 
## 409.2744 409.2744 409.2744

According to the Bayesian information criterion, a model with two clusters describes the data best.

Fitted model:

aucs_diff %>% 
  ggplot(aes(x=diff_of_diffs)) + 
    geom_jitter(aes(y=0, color=first_speaker_type.x), width=0, height=0.001)  +
    ggtitle("Raw data + Components of gaussian mixture") + 
    stat_function(fun = dnorm, args = list(mean = fit2$parameters$mean[1], sd = sqrt(fit2$parameters$variance$sigmasq[1]))) + 
    stat_function(fun = dnorm, args = list(mean = fit2$parameters$mean[2], sd = sqrt(fit2$parameters$variance$sigmasq[2])))
## Warning: Removed 101 row(s) containing missing values (geom_path).

Compute likelihoods based on the adaptation model

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: most_likely_model ~ condition + test_order + first_speaker_type +  
##     first_speaker_type * condition + (1 | workerid)
##    Data: d.post_test
## 
##      AIC      BIC   logLik deviance df.resid 
##      154      171      -71      142      118 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6870 -0.5887 -0.1792  0.5928  1.7182 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  workerid (Intercept) 2.34     1.53    
## Number of obs: 124, groups:  workerid, 62
## 
## Fixed effects:
##                                              Estimate Std. Error z value
## (Intercept)                                   -0.4767     0.3321  -1.435
## conditioncautious                             -1.2705     0.3757  -3.382
## test_orderparallel                            -0.4084     0.3236  -1.262
## first_speaker_typecautious                     0.4631     0.3306   1.401
## conditioncautious:first_speaker_typecautious   0.4238     0.2719   1.559
##                                              Pr(>|z|)    
## (Intercept)                                   0.15123    
## conditioncautious                             0.00072 ***
## test_orderparallel                            0.20701    
## first_speaker_typecautious                    0.16130    
## conditioncautious:first_speaker_typecautious  0.11899    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtnc tst_rd frst__
## conditincts  0.298                     
## tst_rdrprll  0.134  0.245              
## frst_spkr_t -0.221 -0.289 -0.100       
## cndtncts:__ -0.217 -0.402 -0.122  0.213
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: likelihood_ratio ~ condition + test_order + first_speaker_type +  
##     first_speaker_type * condition + (1 | workerid)
##    Data: d.post_test
## 
## REML criterion at convergence: 1646
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.0346 -0.6043 -0.1376  0.4363  2.5545 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  workerid (Intercept) 14000    118.3   
##  Residual             36711    191.6   
## Number of obs: 124, groups:  workerid, 62
## 
## Fixed effects:
##                                              Estimate Std. Error      df
## (Intercept)                                     4.049     22.904  59.000
## conditioncautious                             -74.331     17.242  60.000
## test_orderparallel                             -6.180     22.856  59.000
## first_speaker_typecautious                     41.298     22.892  59.000
## conditioncautious:first_speaker_typecautious   21.163     17.242  60.000
##                                              t value Pr(>|t|)    
## (Intercept)                                    0.177   0.8603    
## conditioncautious                             -4.311 6.14e-05 ***
## test_orderparallel                            -0.270   0.7878    
## first_speaker_typecautious                     1.804   0.0763 .  
## conditioncautious:first_speaker_typecautious   1.227   0.2245    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtnc tst_rd frst__
## conditincts  0.000                     
## tst_rdrprll  0.032  0.000              
## frst_spkr_t -0.065  0.000 -0.002       
## cndtncts:__  0.000 -0.065  0.000  0.000
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: likelihood_ratio ~ condition + test_order + first_speaker_type +  
##     prior_likelihood_ratio + first_speaker_type * condition +  
##     (1 | workerid)
##    Data: d.post_test
## 
## REML criterion at convergence: 1647.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9845 -0.5693 -0.1259  0.4594  2.6164 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  workerid (Intercept) 14379    119.9   
##  Residual             36711    191.6   
## Number of obs: 124, groups:  workerid, 62
## 
## Fixed effects:
##                                               Estimate Std. Error        df
## (Intercept)                                   12.72944   27.71509  58.00000
## conditioncautious                            -74.33107   17.24211  60.00000
## test_orderparallel                            -1.73800   24.30395  58.00000
## first_speaker_typecautious                    41.68218   23.03583  58.00000
## prior_likelihood_ratio                         0.09466    0.16801  58.00000
## conditioncautious:first_speaker_typecautious  21.16343   17.24211  60.00000
##                                              t value Pr(>|t|)    
## (Intercept)                                    0.459   0.6477    
## conditioncautious                             -4.311 6.14e-05 ***
## test_orderparallel                            -0.072   0.9432    
## first_speaker_typecautious                     1.809   0.0756 .  
## prior_likelihood_ratio                         0.563   0.5753    
## conditioncautious:first_speaker_typecautious   1.227   0.2245    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cndtnc tst_rd frst__ prr_l_
## conditincts  0.000                            
## tst_rdrprll  0.206  0.000                     
## frst_spkr_t -0.037  0.000  0.008              
## prr_lklhd_r  0.556  0.000  0.324  0.030       
## cndtncts:__  0.000 -0.065  0.000  0.000  0.000
## Data: d.post_test
## Models:
## model1: likelihood_ratio ~ condition + test_order + first_speaker_type + first_speaker_type * condition + (1 | workerid)
## model2: likelihood_ratio ~ condition + test_order + first_speaker_type + prior_likelihood_ratio + first_speaker_type * condition + (1 | workerid)
##        npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)
## model1    7 1699.3 1719.0 -842.64   1685.3                     
## model2    8 1700.9 1723.5 -842.47   1684.9 0.3384  1     0.5608

List of adapters:

workerid first_speaker_type test_order noticed_manipulation cautious_count confident_count aligned_count first_adaptation_speaker_count
1507 cautious reverse 0 1 1 2 1
1513 confident parallel 1 1 1 2 1
1522 confident reverse 1 1 1 2 1
1524 confident reverse 0 1 1 2 1
1525 cautious reverse 1 1 1 2 1
1527 cautious parallel 1 1 1 2 1
1528 confident parallel 1 1 1 2 1
1530 cautious reverse 1 1 1 2 1
1532 cautious parallel 0 1 1 2 1
1537 confident parallel 1 1 1 2 1
1539 cautious reverse 1 1 1 2 1
1541 cautious parallel 1 1 1 2 1
1543 confident reverse 0 1 1 2 1
1545 confident parallel 0 1 1 2 1
1547 cautious reverse 1 1 1 2 1
1548 cautious parallel 1 1 1 2 1
1551 confident reverse 0 1 1 2 1
1552 confident parallel 1 1 1 2 1
1553 confident parallel 0 1 1 2 1
1558 confident reverse 1 1 1 2 1
1559 confident reverse 1 1 1 2 1
1560 confident parallel 1 1 1 2 1
1564 cautious parallel 0 1 1 2 1
1566 confident reverse 1 1 1 2 1
1571 cautious reverse 0 1 1 2 1

List of reverse adapters:

workerid first_speaker_type test_order noticed_manipulation cautious_count confident_count aligned_count first_adaptation_speaker_count
1521 cautious parallel 0 1 1 0 1
1546 cautious reverse 0 1 1 0 1